{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(12345)\n",
    "plt.rc('figure', figsize=(10, 6))\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:05.065388Z",
     "end_time": "2024-04-17T13:23:07.973724Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "my_arr = np.arange(1_000_000)\n",
    "my_list = list(range(1_000_000))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:05.642321Z",
     "end_time": "2024-04-17T13:23:07.989233Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.64 ms ± 14.5 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n",
      "57.9 ms ± 311 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit my_arr2=my_arr * 2\n",
    "%timeit my_list2=[x * 2 for x in my_list]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:05.659975Z",
     "end_time": "2024-04-17T13:23:23.902293Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.1 NumPy的ndarray:一种多维数组对象"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.2047,  0.4789, -0.5194],\n       [-0.5557,  1.9658,  1.3934]])"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.randn(2, 3)\n",
    "data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.903294Z",
     "end_time": "2024-04-17T13:23:23.915328Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-2.0471,  4.7894, -5.1944],\n       [-5.5573, 19.6578, 13.9341]])"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data * 10"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.918334Z",
     "end_time": "2024-04-17T13:23:23.974814Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.4094,  0.9579, -1.0389],\n       [-1.1115,  3.9316,  2.7868]])"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data + data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.924511Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "(2, 3)"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.929871Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('float64')"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.936495Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 创建ndarray"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [
    {
     "data": {
      "text/plain": "array([6. , 7.5, 8. , 0. , 1. ])"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.940852Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1, 2, 3, 4],\n       [5, 6, 7, 8]])"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.947564Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "2"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.ndim"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.953593Z",
     "end_time": "2024-04-17T13:23:23.976816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "(2, 4)"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.shape"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.959287Z",
     "end_time": "2024-04-17T13:23:23.977816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('float64')"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.963500Z",
     "end_time": "2024-04-17T13:23:23.977816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('int32')"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.970377Z",
     "end_time": "2024-04-17T13:23:23.977816Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.976816Z",
     "end_time": "2024-04-17T13:23:23.994846Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0., 0., 0., 0., 0., 0.],\n       [0., 0., 0., 0., 0., 0.],\n       [0., 0., 0., 0., 0., 0.]])"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3, 6))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.982107Z",
     "end_time": "2024-04-17T13:23:23.996190Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[9.1563e-312, 3.1620e-322],\n        [0.0000e+000, 0.0000e+000],\n        [8.0110e-307, 2.0233e-052]],\n\n       [[6.0089e-067, 2.1114e-052],\n        [4.4997e+174, 1.6737e-076],\n        [1.9682e+160, 9.0487e-067]]])"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((2, 3, 2))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.988353Z",
     "end_time": "2024-04-17T13:23:23.996190Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.993846Z",
     "end_time": "2024-04-17T13:23:24.014561Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### ndarray的数据类型"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [
    {
     "data": {
      "text/plain": "array([1., 2., 3.])"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:23.998193Z",
     "end_time": "2024-04-17T13:23:24.209674Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('float64')"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.007274Z",
     "end_time": "2024-04-17T13:23:24.209674Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "array([1, 2, 3])"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "arr2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.012561Z",
     "end_time": "2024-04-17T13:23:24.211384Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('int32')"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.020428Z",
     "end_time": "2024-04-17T13:23:24.211384Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('int32')"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.027085Z",
     "end_time": "2024-04-17T13:23:24.211384Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('float64')"
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.032690Z",
     "end_time": "2024-04-17T13:23:24.212389Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 3.7, -1.2, -2.6,  0.5, 12.9, 10.1])"
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([3.7, -1.2, -2.6, 0.5, 12.9, 10.1])\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.038648Z",
     "end_time": "2024-04-17T13:23:24.213389Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 3, -1, -2,  0, 12, 10])"
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.astype(np.int32)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.045315Z",
     "end_time": "2024-04-17T13:23:24.213389Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "data": {
      "text/plain": "array([b'1.25', b'-9.6', b'42'], dtype='|S4')"
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings = np.array(['1.25', '-9.6', '42'], dtype=np.string_)\n",
    "numeric_strings"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.055192Z",
     "end_time": "2024-04-17T13:23:24.213389Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('S4')"
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.060849Z",
     "end_time": "2024-04-17T13:23:24.213389Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 1.25, -9.6 , 42.  ])"
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeric_strings.astype(float)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.066194Z",
     "end_time": "2024-04-17T13:23:24.214390Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_array = np.arange(10)\n",
    "calibers = np.array([.22, .27, .357, .44, .5])\n",
    "int_array.astype(calibers.dtype)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.072921Z",
     "end_time": "2024-04-17T13:23:24.214390Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "array([         0, 1075314688,          0, 1075707904,          0,\n       1075838976,          0, 1072693248], dtype=uint32)"
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_uint32 = np.empty(8, dtype='u4')\n",
    "empty_uint32"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.079880Z",
     "end_time": "2024-04-17T13:23:24.214390Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [
    {
     "data": {
      "text/plain": "dtype('uint32')"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "empty_uint32.dtype"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.085737Z",
     "end_time": "2024-04-17T13:23:24.214390Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### NumPy数组的运算"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1., 2., 3.],\n       [4., 5., 6.]])"
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.090712Z",
     "end_time": "2024-04-17T13:23:24.214390Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 1.,  4.,  9.],\n       [16., 25., 36.]])"
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr * arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.098071Z",
     "end_time": "2024-04-17T13:23:24.248677Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0., 0., 0.],\n       [0., 0., 0.]])"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr - arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.106543Z",
     "end_time": "2024-04-17T13:23:24.264563Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1.    , 0.5   , 0.3333],\n       [0.25  , 0.2   , 0.1667]])"
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.113137Z",
     "end_time": "2024-04-17T13:23:24.264563Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1.    , 1.4142, 1.7321],\n       [2.    , 2.2361, 2.4495]])"
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr ** 0.5"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.117539Z",
     "end_time": "2024-04-17T13:23:24.264563Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0.,  4.,  1.],\n       [ 7.,  2., 12.]])"
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.125391Z",
     "end_time": "2024-04-17T13:23:24.264563Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[False,  True, False],\n       [ True, False,  True]])"
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 > arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.131486Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 基本的索引和切片"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.138637Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "outputs": [
    {
     "data": {
      "text/plain": "5"
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.153241Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "outputs": [
    {
     "data": {
      "text/plain": "array([5, 6, 7])"
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.158697Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] = 12\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.164439Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "outputs": [
    {
     "data": {
      "text/plain": "array([12, 12, 12])"
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice = arr[5:8]\n",
    "arr_slice"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.170981Z",
     "end_time": "2024-04-17T13:23:24.265568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "outputs": [
    {
     "data": {
      "text/plain": "array([    0,     1,     2,     3,     4,    12, 12345,    12,     8,\n           9])"
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[1] = 12345\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.175405Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr_slice[:] = 64\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.182100Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "outputs": [
    {
     "data": {
      "text/plain": "array([7, 8, 9])"
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "arr2d[2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.187916Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "outputs": [
    {
     "data": {
      "text/plain": "3"
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0][2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.197134Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "outputs": [
    {
     "data": {
      "text/plain": "3"
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[0, 2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.202925Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 1,  2,  3],\n        [ 4,  5,  6]],\n\n       [[ 7,  8,  9],\n        [10, 11, 12]]])"
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.207673Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1, 2, 3],\n       [4, 5, 6]])"
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.214390Z",
     "end_time": "2024-04-17T13:23:24.266569Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[42, 42, 42],\n        [42, 42, 42]],\n\n       [[ 7,  8,  9],\n        [10, 11, 12]]])"
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "old_values = arr3d[0].copy()\n",
    "arr3d[0] = 42\n",
    "arr3d"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.221014Z",
     "end_time": "2024-04-17T13:23:24.267568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 1,  2,  3],\n        [ 4,  5,  6]],\n\n       [[ 7,  8,  9],\n        [10, 11, 12]]])"
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = old_values\n",
    "arr3d"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.226451Z",
     "end_time": "2024-04-17T13:23:24.267568Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "outputs": [
    {
     "data": {
      "text/plain": "array([7, 8, 9])"
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.232276Z",
     "end_time": "2024-04-17T13:23:24.572618Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 7,  8,  9],\n       [10, 11, 12]])"
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = arr3d[1]\n",
    "x"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.239225Z",
     "end_time": "2024-04-17T13:23:24.573618Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "outputs": [
    {
     "data": {
      "text/plain": "array([7, 8, 9])"
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.251680Z",
     "end_time": "2024-04-17T13:23:24.573618Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 切片索引"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0,  1,  2,  3,  4, 64, 64, 64,  8,  9])"
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.257724Z",
     "end_time": "2024-04-17T13:23:24.573618Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 1,  2,  3,  4, 64])"
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[1:6]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.261608Z",
     "end_time": "2024-04-17T13:23:24.573618Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1, 2, 3],\n       [4, 5, 6],\n       [7, 8, 9]])"
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.268569Z",
     "end_time": "2024-04-17T13:23:24.573618Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1, 2, 3],\n       [4, 5, 6]])"
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.273905Z",
     "end_time": "2024-04-17T13:23:24.574619Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[2, 3],\n       [5, 6]])"
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.278521Z",
     "end_time": "2024-04-17T13:23:24.575620Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "outputs": [
    {
     "data": {
      "text/plain": "array([4, 5])"
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[1, :2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.284728Z",
     "end_time": "2024-04-17T13:23:24.575620Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "outputs": [
    {
     "data": {
      "text/plain": "array([3, 6])"
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 2]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.290688Z",
     "end_time": "2024-04-17T13:23:24.576622Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1],\n       [4],\n       [7]])"
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:, :1]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.296002Z",
     "end_time": "2024-04-17T13:23:24.576622Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1, 0, 0],\n       [4, 0, 0],\n       [7, 8, 9]])"
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d[:2, 1:] = 0\n",
    "arr2d"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.301450Z",
     "end_time": "2024-04-17T13:23:24.576886Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 布尔型索引"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "outputs": [
    {
     "data": {
      "text/plain": "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "names"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.307389Z",
     "end_time": "2024-04-17T13:23:24.576886Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n       [ 1.0072, -1.2962,  0.275 ,  0.2289],\n       [ 1.3529,  0.8864, -2.0016, -0.3718],\n       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n       [ 3.2489, -1.0212, -0.5771,  0.1241],\n       [ 0.3026,  0.5238,  0.0009,  1.3438],\n       [-0.7135, -0.8312, -2.3702, -1.8608]])"
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.randn(7, 4)\n",
    "data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.313940Z",
     "end_time": "2024-04-17T13:23:24.576886Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ True, False, False,  True, False, False, False])"
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.318159Z",
     "end_time": "2024-04-17T13:23:24.576886Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n       [ 1.669 , -0.4386, -0.5397,  0.477 ]])"
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob']"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.325106Z",
     "end_time": "2024-04-17T13:23:24.653900Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0.769 ,  1.2464],\n       [-0.5397,  0.477 ]])"
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob', 2:]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.332258Z",
     "end_time": "2024-04-17T13:23:24.693906Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "outputs": [
    {
     "data": {
      "text/plain": "array([1.2464, 0.477 ])"
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names == 'Bob', 3]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.337726Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "outputs": [
    {
     "data": {
      "text/plain": "array([False,  True,  True, False,  True,  True,  True])"
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names != 'Bob'"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.344698Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n       [ 1.3529,  0.8864, -2.0016, -0.3718],\n       [ 3.2489, -1.0212, -0.5771,  0.1241],\n       [ 0.3026,  0.5238,  0.0009,  1.3438],\n       [-0.7135, -0.8312, -2.3702, -1.8608]])"
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != 'Bob']"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.350269Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n       [ 1.3529,  0.8864, -2.0016, -0.3718],\n       [ 3.2489, -1.0212, -0.5771,  0.1241],\n       [ 0.3026,  0.5238,  0.0009,  1.3438],\n       [-0.7135, -0.8312, -2.3702, -1.8608]])"
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[~(names == 'Bob')]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.357012Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 1.0072, -1.2962,  0.275 ,  0.2289],\n       [ 1.3529,  0.8864, -2.0016, -0.3718],\n       [ 3.2489, -1.0212, -0.5771,  0.1241],\n       [ 0.3026,  0.5238,  0.0009,  1.3438],\n       [-0.7135, -0.8312, -2.3702, -1.8608]])"
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cond = names == 'Bob'\n",
    "data[~cond]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.364265Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ True, False,  True,  True,  True, False, False])"
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = (names == 'Bob') | (names == 'Will')\n",
    "mask"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.368775Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0.0929,  0.2817,  0.769 ,  1.2464],\n       [ 1.3529,  0.8864, -2.0016, -0.3718],\n       [ 1.669 , -0.4386, -0.5397,  0.477 ],\n       [ 3.2489, -1.0212, -0.5771,  0.1241]])"
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[mask]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.374260Z",
     "end_time": "2024-04-17T13:23:24.694908Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0.0929, 0.2817, 0.769 , 1.2464],\n       [1.0072, 0.    , 0.275 , 0.2289],\n       [1.3529, 0.8864, 0.    , 0.    ],\n       [1.669 , 0.    , 0.    , 0.477 ],\n       [3.2489, 0.    , 0.    , 0.1241],\n       [0.3026, 0.5238, 0.0009, 1.3438],\n       [0.    , 0.    , 0.    , 0.    ]])"
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data < 0] = 0\n",
    "data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.379558Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[7.    , 7.    , 7.    , 7.    ],\n       [1.0072, 0.    , 0.275 , 0.2289],\n       [7.    , 7.    , 7.    , 7.    ],\n       [7.    , 7.    , 7.    , 7.    ],\n       [7.    , 7.    , 7.    , 7.    ],\n       [0.3026, 0.5238, 0.0009, 1.3438],\n       [0.    , 0.    , 0.    , 0.    ]])"
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[names != 'Joe'] = 7\n",
    "data"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.384775Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 花式索引"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1.  , 0.  , 0.16, 1.  ],\n       [1.  , 0.  , 0.  , 1.  ],\n       [1.  , 1.  , 0.  , 1.  ],\n       [0.  , 1.  , 0.  , 1.  ],\n       [0.  , 1.  , 1.  , 1.  ],\n       [0.  , 0.  , 1.  , 1.  ],\n       [1.  , 0.  , 1.  , 1.  ],\n       [1.  , 0.  , 0.75, 1.  ]])"
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.empty((8, 4))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.392357Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0., 0., 0., 0.],\n       [1., 1., 1., 1.],\n       [2., 2., 2., 2.],\n       [3., 3., 3., 3.],\n       [4., 4., 4., 4.],\n       [5., 5., 5., 5.],\n       [6., 6., 6., 6.],\n       [7., 7., 7., 7.]])"
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    arr[i] = i\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.395989Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[4., 4., 4., 4.],\n       [3., 3., 3., 3.],\n       [0., 0., 0., 0.],\n       [6., 6., 6., 6.]])"
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[4, 3, 0, 6]]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.401739Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[5., 5., 5., 5.],\n       [3., 3., 3., 3.],\n       [1., 1., 1., 1.]])"
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[-3, -5, -7]]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.410797Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  2,  3],\n       [ 4,  5,  6,  7],\n       [ 8,  9, 10, 11],\n       [12, 13, 14, 15],\n       [16, 17, 18, 19],\n       [20, 21, 22, 23],\n       [24, 25, 26, 27],\n       [28, 29, 30, 31]])"
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.416960Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 4, 23, 29, 10])"
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2], [0, 3, 1, 2]]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.425121Z",
     "end_time": "2024-04-17T13:23:24.695909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 4,  7,  5,  6],\n       [20, 23, 21, 22],\n       [28, 31, 29, 30],\n       [ 8, 11,  9, 10]])"
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.431544Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 数组转置和轴对换"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  2,  3,  4],\n       [ 5,  6,  7,  8,  9],\n       [10, 11, 12, 13, 14]])"
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.438180Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  5, 10],\n       [ 1,  6, 11],\n       [ 2,  7, 12],\n       [ 3,  8, 13],\n       [ 4,  9, 14]])"
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.T"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.444079Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.8608,  0.5601, -1.2659],\n       [ 0.1198, -1.0635,  0.3329],\n       [-2.3594, -0.1995, -1.542 ],\n       [-0.9707, -1.307 ,  0.2863],\n       [ 0.378 , -0.7539,  0.3313],\n       [ 1.3497,  0.0699,  0.2467]])"
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6, 3)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.450012Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 9.2291,  0.9394,  4.948 ],\n       [ 0.9394,  3.7662, -1.3622],\n       [ 4.948 , -1.3622,  4.3437]])"
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(arr.T, arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.456504Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 4,  5,  6,  7]],\n\n       [[ 8,  9, 10, 11],\n        [12, 13, 14, 15]]])"
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(16).reshape((2, 2, 4))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.463264Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 8,  9, 10, 11]],\n\n       [[ 4,  5,  6,  7],\n        [12, 13, 14, 15]]])"
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.transpose((1, 0, 2))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.470309Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 0,  1,  2,  3],\n        [ 4,  5,  6,  7]],\n\n       [[ 8,  9, 10, 11],\n        [12, 13, 14, 15]]])"
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.476387Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[[ 0,  4],\n        [ 1,  5],\n        [ 2,  6],\n        [ 3,  7]],\n\n       [[ 8, 12],\n        [ 9, 13],\n        [10, 14],\n        [11, 15]]])"
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.swapaxes(1, 2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.482231Z",
     "end_time": "2024-04-17T13:23:24.696909Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.2 通用函数：快速的元素级数组函数"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.487993Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0.    , 1.    , 1.4142, 1.7321, 2.    , 2.2361, 2.4495, 2.6458,\n       2.8284, 3.    ])"
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.493092Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "outputs": [
    {
     "data": {
      "text/plain": "array([   1.    ,    2.7183,    7.3891,   20.0855,   54.5982,  148.4132,\n        403.4288, 1096.6332, 2980.958 , 8103.0839])"
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.498762Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-0.0119,  1.0048,  1.3272, -0.9193, -1.5491,  0.0222,  0.7584,\n       -0.6605])"
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randn(8)\n",
    "x"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.504770Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0.8626, -0.01  ,  0.05  ,  0.6702,  0.853 , -0.9559, -0.0235,\n       -2.3042])"
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.random.randn(8)\n",
    "y"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.509843Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0.8626,  1.0048,  1.3272,  0.6702,  0.853 ,  0.0222,  0.7584,\n       -0.6605])"
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.maximum(x, y)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.518650Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(7) * 5\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.525341Z",
     "end_time": "2024-04-17T13:23:24.697909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "outputs": [],
   "source": [
    "remainder, whole_part = np.modf(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.532037Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-0.2623, -0.0915, -0.663 ,  0.3731,  0.6182,  0.45  ,  0.0077])"
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remainder"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.536042Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-3., -6., -6.,  5.,  3.,  3.,  5.])"
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whole_part"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.542527Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-3.2623, -6.0915, -6.663 ,  5.3731,  3.6182,  3.45  ,  5.0077])"
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.547170Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\AppData\\Local\\Temp\\ipykernel_21368\\1450069282.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  np.sqrt(arr)\n"
     ]
    },
    {
     "data": {
      "text/plain": "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.553420Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\AppData\\Local\\Temp\\ipykernel_21368\\1787379640.py:1: RuntimeWarning: invalid value encountered in sqrt\n",
      "  np.sqrt(arr, arr)\n"
     ]
    },
    {
     "data": {
      "text/plain": "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(arr, arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.560173Z",
     "end_time": "2024-04-17T13:23:24.698909Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "outputs": [
    {
     "data": {
      "text/plain": "array([   nan,    nan,    nan, 2.318 , 1.9022, 1.8574, 2.2378])"
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.564417Z",
     "end_time": "2024-04-17T13:23:24.699910Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.3利用数组进行数据处理"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-5.  , -4.99, -4.98, -4.97, -4.96, -4.95, -4.94, -4.93, -4.92,\n       -4.91, -4.9 , -4.89, -4.88, -4.87, -4.86, -4.85, -4.84, -4.83,\n       -4.82, -4.81, -4.8 , -4.79, -4.78, -4.77, -4.76, -4.75, -4.74,\n       -4.73, -4.72, -4.71, -4.7 , -4.69, -4.68, -4.67, -4.66, -4.65,\n       -4.64, -4.63, -4.62, -4.61, -4.6 , -4.59, -4.58, -4.57, -4.56,\n       -4.55, -4.54, -4.53, -4.52, -4.51, -4.5 , -4.49, -4.48, -4.47,\n       -4.46, -4.45, -4.44, -4.43, -4.42, -4.41, -4.4 , -4.39, -4.38,\n       -4.37, -4.36, -4.35, -4.34, -4.33, -4.32, -4.31, -4.3 , -4.29,\n       -4.28, -4.27, -4.26, -4.25, -4.24, -4.23, -4.22, -4.21, -4.2 ,\n       -4.19, -4.18, -4.17, -4.16, -4.15, -4.14, -4.13, -4.12, -4.11,\n       -4.1 , -4.09, -4.08, -4.07, -4.06, -4.05, -4.04, -4.03, -4.02,\n       -4.01, -4.  , -3.99, -3.98, -3.97, -3.96, -3.95, -3.94, -3.93,\n       -3.92, -3.91, -3.9 , -3.89, -3.88, -3.87, -3.86, -3.85, -3.84,\n       -3.83, -3.82, -3.81, -3.8 , -3.79, -3.78, -3.77, -3.76, -3.75,\n       -3.74, -3.73, -3.72, -3.71, -3.7 , -3.69, -3.68, -3.67, -3.66,\n       -3.65, -3.64, -3.63, -3.62, -3.61, -3.6 , -3.59, -3.58, -3.57,\n       -3.56, -3.55, -3.54, -3.53, -3.52, -3.51, -3.5 , -3.49, -3.48,\n       -3.47, -3.46, -3.45, -3.44, -3.43, -3.42, -3.41, -3.4 , -3.39,\n       -3.38, -3.37, -3.36, -3.35, -3.34, -3.33, -3.32, -3.31, -3.3 ,\n       -3.29, -3.28, -3.27, -3.26, -3.25, -3.24, -3.23, -3.22, -3.21,\n       -3.2 , -3.19, -3.18, -3.17, -3.16, -3.15, -3.14, -3.13, -3.12,\n       -3.11, -3.1 , -3.09, -3.08, -3.07, -3.06, -3.05, -3.04, -3.03,\n       -3.02, -3.01, -3.  , -2.99, -2.98, -2.97, -2.96, -2.95, -2.94,\n       -2.93, -2.92, -2.91, -2.9 , -2.89, -2.88, -2.87, -2.86, -2.85,\n       -2.84, -2.83, -2.82, -2.81, -2.8 , -2.79, -2.78, -2.77, -2.76,\n       -2.75, -2.74, -2.73, -2.72, -2.71, -2.7 , -2.69, -2.68, -2.67,\n       -2.66, -2.65, -2.64, -2.63, -2.62, -2.61, -2.6 , -2.59, -2.58,\n       -2.57, -2.56, -2.55, -2.54, -2.53, -2.52, -2.51, -2.5 , -2.49,\n       -2.48, -2.47, -2.46, -2.45, -2.44, -2.43, -2.42, -2.41, -2.4 ,\n       -2.39, -2.38, -2.37, -2.36, -2.35, -2.34, -2.33, -2.32, -2.31,\n       -2.3 , -2.29, -2.28, -2.27, -2.26, -2.25, -2.24, -2.23, -2.22,\n       -2.21, -2.2 , -2.19, -2.18, -2.17, -2.16, -2.15, -2.14, -2.13,\n       -2.12, -2.11, -2.1 , -2.09, -2.08, -2.07, -2.06, -2.05, -2.04,\n       -2.03, -2.02, -2.01, -2.  , -1.99, -1.98, -1.97, -1.96, -1.95,\n       -1.94, -1.93, -1.92, -1.91, -1.9 , -1.89, -1.88, -1.87, -1.86,\n       -1.85, -1.84, -1.83, -1.82, -1.81, -1.8 , -1.79, -1.78, -1.77,\n       -1.76, -1.75, -1.74, -1.73, -1.72, -1.71, -1.7 , -1.69, -1.68,\n       -1.67, -1.66, -1.65, -1.64, -1.63, -1.62, -1.61, -1.6 , -1.59,\n       -1.58, -1.57, -1.56, -1.55, -1.54, -1.53, -1.52, -1.51, -1.5 ,\n       -1.49, -1.48, -1.47, -1.46, -1.45, -1.44, -1.43, -1.42, -1.41,\n       -1.4 , -1.39, -1.38, -1.37, -1.36, -1.35, -1.34, -1.33, -1.32,\n       -1.31, -1.3 , -1.29, -1.28, -1.27, -1.26, -1.25, -1.24, -1.23,\n       -1.22, -1.21, -1.2 , -1.19, -1.18, -1.17, -1.16, -1.15, -1.14,\n       -1.13, -1.12, -1.11, -1.1 , -1.09, -1.08, -1.07, -1.06, -1.05,\n       -1.04, -1.03, -1.02, -1.01, -1.  , -0.99, -0.98, -0.97, -0.96,\n       -0.95, -0.94, -0.93, -0.92, -0.91, -0.9 , -0.89, -0.88, -0.87,\n       -0.86, -0.85, -0.84, -0.83, -0.82, -0.81, -0.8 , -0.79, -0.78,\n       -0.77, -0.76, -0.75, -0.74, -0.73, -0.72, -0.71, -0.7 , -0.69,\n       -0.68, -0.67, -0.66, -0.65, -0.64, -0.63, -0.62, -0.61, -0.6 ,\n       -0.59, -0.58, -0.57, -0.56, -0.55, -0.54, -0.53, -0.52, -0.51,\n       -0.5 , -0.49, -0.48, -0.47, -0.46, -0.45, -0.44, -0.43, -0.42,\n       -0.41, -0.4 , -0.39, -0.38, -0.37, -0.36, -0.35, -0.34, -0.33,\n       -0.32, -0.31, -0.3 , -0.29, -0.28, -0.27, -0.26, -0.25, -0.24,\n       -0.23, -0.22, -0.21, -0.2 , -0.19, -0.18, -0.17, -0.16, -0.15,\n       -0.14, -0.13, -0.12, -0.11, -0.1 , -0.09, -0.08, -0.07, -0.06,\n       -0.05, -0.04, -0.03, -0.02, -0.01, -0.  ,  0.01,  0.02,  0.03,\n        0.04,  0.05,  0.06,  0.07,  0.08,  0.09,  0.1 ,  0.11,  0.12,\n        0.13,  0.14,  0.15,  0.16,  0.17,  0.18,  0.19,  0.2 ,  0.21,\n        0.22,  0.23,  0.24,  0.25,  0.26,  0.27,  0.28,  0.29,  0.3 ,\n        0.31,  0.32,  0.33,  0.34,  0.35,  0.36,  0.37,  0.38,  0.39,\n        0.4 ,  0.41,  0.42,  0.43,  0.44,  0.45,  0.46,  0.47,  0.48,\n        0.49,  0.5 ,  0.51,  0.52,  0.53,  0.54,  0.55,  0.56,  0.57,\n        0.58,  0.59,  0.6 ,  0.61,  0.62,  0.63,  0.64,  0.65,  0.66,\n        0.67,  0.68,  0.69,  0.7 ,  0.71,  0.72,  0.73,  0.74,  0.75,\n        0.76,  0.77,  0.78,  0.79,  0.8 ,  0.81,  0.82,  0.83,  0.84,\n        0.85,  0.86,  0.87,  0.88,  0.89,  0.9 ,  0.91,  0.92,  0.93,\n        0.94,  0.95,  0.96,  0.97,  0.98,  0.99,  1.  ,  1.01,  1.02,\n        1.03,  1.04,  1.05,  1.06,  1.07,  1.08,  1.09,  1.1 ,  1.11,\n        1.12,  1.13,  1.14,  1.15,  1.16,  1.17,  1.18,  1.19,  1.2 ,\n        1.21,  1.22,  1.23,  1.24,  1.25,  1.26,  1.27,  1.28,  1.29,\n        1.3 ,  1.31,  1.32,  1.33,  1.34,  1.35,  1.36,  1.37,  1.38,\n        1.39,  1.4 ,  1.41,  1.42,  1.43,  1.44,  1.45,  1.46,  1.47,\n        1.48,  1.49,  1.5 ,  1.51,  1.52,  1.53,  1.54,  1.55,  1.56,\n        1.57,  1.58,  1.59,  1.6 ,  1.61,  1.62,  1.63,  1.64,  1.65,\n        1.66,  1.67,  1.68,  1.69,  1.7 ,  1.71,  1.72,  1.73,  1.74,\n        1.75,  1.76,  1.77,  1.78,  1.79,  1.8 ,  1.81,  1.82,  1.83,\n        1.84,  1.85,  1.86,  1.87,  1.88,  1.89,  1.9 ,  1.91,  1.92,\n        1.93,  1.94,  1.95,  1.96,  1.97,  1.98,  1.99,  2.  ,  2.01,\n        2.02,  2.03,  2.04,  2.05,  2.06,  2.07,  2.08,  2.09,  2.1 ,\n        2.11,  2.12,  2.13,  2.14,  2.15,  2.16,  2.17,  2.18,  2.19,\n        2.2 ,  2.21,  2.22,  2.23,  2.24,  2.25,  2.26,  2.27,  2.28,\n        2.29,  2.3 ,  2.31,  2.32,  2.33,  2.34,  2.35,  2.36,  2.37,\n        2.38,  2.39,  2.4 ,  2.41,  2.42,  2.43,  2.44,  2.45,  2.46,\n        2.47,  2.48,  2.49,  2.5 ,  2.51,  2.52,  2.53,  2.54,  2.55,\n        2.56,  2.57,  2.58,  2.59,  2.6 ,  2.61,  2.62,  2.63,  2.64,\n        2.65,  2.66,  2.67,  2.68,  2.69,  2.7 ,  2.71,  2.72,  2.73,\n        2.74,  2.75,  2.76,  2.77,  2.78,  2.79,  2.8 ,  2.81,  2.82,\n        2.83,  2.84,  2.85,  2.86,  2.87,  2.88,  2.89,  2.9 ,  2.91,\n        2.92,  2.93,  2.94,  2.95,  2.96,  2.97,  2.98,  2.99,  3.  ,\n        3.01,  3.02,  3.03,  3.04,  3.05,  3.06,  3.07,  3.08,  3.09,\n        3.1 ,  3.11,  3.12,  3.13,  3.14,  3.15,  3.16,  3.17,  3.18,\n        3.19,  3.2 ,  3.21,  3.22,  3.23,  3.24,  3.25,  3.26,  3.27,\n        3.28,  3.29,  3.3 ,  3.31,  3.32,  3.33,  3.34,  3.35,  3.36,\n        3.37,  3.38,  3.39,  3.4 ,  3.41,  3.42,  3.43,  3.44,  3.45,\n        3.46,  3.47,  3.48,  3.49,  3.5 ,  3.51,  3.52,  3.53,  3.54,\n        3.55,  3.56,  3.57,  3.58,  3.59,  3.6 ,  3.61,  3.62,  3.63,\n        3.64,  3.65,  3.66,  3.67,  3.68,  3.69,  3.7 ,  3.71,  3.72,\n        3.73,  3.74,  3.75,  3.76,  3.77,  3.78,  3.79,  3.8 ,  3.81,\n        3.82,  3.83,  3.84,  3.85,  3.86,  3.87,  3.88,  3.89,  3.9 ,\n        3.91,  3.92,  3.93,  3.94,  3.95,  3.96,  3.97,  3.98,  3.99,\n        4.  ,  4.01,  4.02,  4.03,  4.04,  4.05,  4.06,  4.07,  4.08,\n        4.09,  4.1 ,  4.11,  4.12,  4.13,  4.14,  4.15,  4.16,  4.17,\n        4.18,  4.19,  4.2 ,  4.21,  4.22,  4.23,  4.24,  4.25,  4.26,\n        4.27,  4.28,  4.29,  4.3 ,  4.31,  4.32,  4.33,  4.34,  4.35,\n        4.36,  4.37,  4.38,  4.39,  4.4 ,  4.41,  4.42,  4.43,  4.44,\n        4.45,  4.46,  4.47,  4.48,  4.49,  4.5 ,  4.51,  4.52,  4.53,\n        4.54,  4.55,  4.56,  4.57,  4.58,  4.59,  4.6 ,  4.61,  4.62,\n        4.63,  4.64,  4.65,  4.66,  4.67,  4.68,  4.69,  4.7 ,  4.71,\n        4.72,  4.73,  4.74,  4.75,  4.76,  4.77,  4.78,  4.79,  4.8 ,\n        4.81,  4.82,  4.83,  4.84,  4.85,  4.86,  4.87,  4.88,  4.89,\n        4.9 ,  4.91,  4.92,  4.93,  4.94,  4.95,  4.96,  4.97,  4.98,\n        4.99])"
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points = np.arange(-5, 5, 0.01)\n",
    "points"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.569618Z",
     "end_time": "2024-04-17T13:23:24.699910Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],\n       ...,\n       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],\n       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],\n       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]])"
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs, ys = np.meshgrid(points, points)\n",
    "ys"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.580396Z",
     "end_time": "2024-04-17T13:23:24.700910Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[7.0711, 7.064 , 7.0569, ..., 7.0499, 7.0569, 7.064 ],\n       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569],\n       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n       ...,\n       [7.0499, 7.0428, 7.0357, ..., 7.0286, 7.0357, 7.0428],\n       [7.0569, 7.0499, 7.0428, ..., 7.0357, 7.0428, 7.0499],\n       [7.064 , 7.0569, 7.0499, ..., 7.0428, 7.0499, 7.0569]])"
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)\n",
    "z"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.590387Z",
     "end_time": "2024-04-17T13:23:24.701910Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'Image plot of $\\\\sqrt{x^2 + y^2}$ for a grid of values')"
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 2 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.imshow(z, cmap=plt.cm.gray)\n",
    "plt.colorbar()\n",
    "plt.title(\"Image plot of $\\sqrt{x^2 + y^2}$ for a grid of values\")"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:24.607889Z",
     "end_time": "2024-04-17T13:23:25.147085Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 将条件逻辑表述为数组运算"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "outputs": [
    {
     "data": {
      "text/plain": "[1.1, 2.2, 1.3, 1.4, 2.5]"
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xarr = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "yarr = np.array([2.1, 2.2, 2.3, 2.4, 2.5])\n",
    "cond = np.array([True, False, True, True, False])\n",
    "result = [(x if c else y) for x, y, c in zip(xarr, yarr, cond)]\n",
    "result"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.044272Z",
     "end_time": "2024-04-17T13:23:25.147085Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "outputs": [
    {
     "data": {
      "text/plain": "array([1.1, 2.2, 1.3, 1.4, 2.5])"
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.where(cond, xarr, yarr)\n",
    "result"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.050493Z",
     "end_time": "2024-04-17T13:23:25.148086Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n       [ 0.2229,  0.0513, -1.1577,  0.8167],\n       [ 0.4336,  1.0107,  1.8249, -0.9975],\n       [ 0.8506, -0.1316,  0.9124,  0.1882]])"
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4, 4)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.057697Z",
     "end_time": "2024-04-17T13:23:25.299375Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[False, False, False, False],\n       [ True,  True, False,  True],\n       [ True,  True,  True, False],\n       [ True, False,  True,  True]])"
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr > 0"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.063323Z",
     "end_time": "2024-04-17T13:23:25.346110Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-2, -2, -2, -2],\n       [ 2,  2, -2,  2],\n       [ 2,  2,  2, -2],\n       [ 2, -2,  2,  2]])"
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, -2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.068914Z",
     "end_time": "2024-04-17T13:23:25.352282Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.5031, -0.6223, -0.9212, -0.7262],\n       [ 2.    ,  2.    , -1.1577,  2.    ],\n       [ 2.    ,  2.    ,  2.    , -0.9975],\n       [ 2.    , -0.1316,  2.    ,  2.    ]])"
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(arr > 0, 2, arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.075754Z",
     "end_time": "2024-04-17T13:23:25.352282Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 数学和统计方法"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  2,  3],\n       [ 4,  5,  6,  7],\n       [ 8,  9, 10, 11],\n       [12, 13, 14, 15],\n       [16, 17, 18, 19]])"
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(20).reshape((5, 4))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.082947Z",
     "end_time": "2024-04-17T13:23:25.352282Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "outputs": [
    {
     "data": {
      "text/plain": "9.5"
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.087412Z",
     "end_time": "2024-04-17T13:23:25.352282Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "outputs": [
    {
     "data": {
      "text/plain": "9.5"
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.094224Z",
     "end_time": "2024-04-17T13:23:25.352282Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "outputs": [
    {
     "data": {
      "text/plain": "190"
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.106277Z",
     "end_time": "2024-04-17T13:23:25.353280Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "outputs": [
    {
     "data": {
      "text/plain": "190"
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.112711Z",
     "end_time": "2024-04-17T13:23:25.353280Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 1.5,  5.5,  9.5, 13.5, 17.5])"
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.mean(axis=1)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.119267Z",
     "end_time": "2024-04-17T13:23:25.353280Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 8.,  9., 10., 11.])"
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(arr, axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.124721Z",
     "end_time": "2024-04-17T13:23:25.353280Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "outputs": [
    {
     "data": {
      "text/plain": "array([40, 45, 50, 55])"
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sum(axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.131470Z",
     "end_time": "2024-04-17T13:23:25.353280Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "outputs": [
    {
     "data": {
      "text/plain": "array([40, 45, 50, 55])"
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(arr, axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.134964Z",
     "end_time": "2024-04-17T13:23:25.354283Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7])"
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(8)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.140939Z",
     "end_time": "2024-04-17T13:23:25.354283Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0,  1,  3,  6, 10, 15, 21, 28])"
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.146085Z",
     "end_time": "2024-04-17T13:23:25.354283Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[0, 1, 2],\n       [3, 4, 5],\n       [6, 7, 8]])"
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(9).reshape((3, 3))\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.151008Z",
     "end_time": "2024-04-17T13:23:25.356533Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  2],\n       [ 3,  5,  7],\n       [ 9, 12, 15]])"
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.159299Z",
     "end_time": "2024-04-17T13:23:25.356533Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  3],\n       [ 3,  7, 12],\n       [ 6, 13, 21]])"
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumsum(axis=1)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.164820Z",
     "end_time": "2024-04-17T13:23:25.356533Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[  0,   0,   0],\n       [  3,  12,  60],\n       [  6,  42, 336]])"
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumprod(axis=1)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.169416Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 0,  1,  2],\n       [ 0,  4, 10],\n       [ 0, 28, 80]])"
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.cumprod(axis=0)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.178533Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 用于布尔型数组的方法"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "outputs": [
    {
     "data": {
      "text/plain": "43"
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(100)\n",
    "(arr > 0).sum()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.184524Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools = np.array([False, False, True, False])\n",
    "bools.any()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.191484Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "outputs": [
    {
     "data": {
      "text/plain": "False"
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bools.all()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.197124Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 排序"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-0.7285,  0.8388,  0.2669,  0.7212,  0.911 , -1.0209])"
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.204081Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "outputs": [
    {
     "data": {
      "text/plain": "array([-1.0209, -0.7285,  0.2669,  0.7212,  0.8388,  0.911 ])"
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.208347Z",
     "end_time": "2024-04-17T13:23:25.546081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-1.4134,  1.2966,  0.2523],\n       [ 1.1275, -0.5684,  0.3094],\n       [-0.5774, -1.1686, -0.825 ],\n       [-2.6444, -0.153 , -0.7519],\n       [-0.1326,  1.4573,  0.6095]])"
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 3)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.214041Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-1.4134,  0.2523,  1.2966],\n       [-0.5684,  0.3094,  1.1275],\n       [-1.1686, -0.825 , -0.5774],\n       [-2.6444, -0.7519, -0.153 ],\n       [-0.1326,  0.6095,  1.4573]])"
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort(1)\n",
    "arr"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.222105Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "outputs": [
    {
     "data": {
      "text/plain": "-1.5311513550102103"
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "large_arr = np.random.randn(1000)\n",
    "large_arr.sort()\n",
    "large_arr[int(0.05 * len(large_arr))]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.229726Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 唯一化以及其它的集合逻辑"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "outputs": [
    {
     "data": {
      "text/plain": "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.235189Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "outputs": [
    {
     "data": {
      "text/plain": "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(names)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.241745Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "outputs": [
    {
     "data": {
      "text/plain": "array([1, 2, 3, 4])"
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ints = np.array([3, 3, 3, 2, 2, 1, 1, 4, 4])\n",
    "np.unique(ints)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.248929Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "outputs": [
    {
     "data": {
      "text/plain": "['Bob', 'Joe', 'Will']"
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(set(names))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.254889Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ True, False, False,  True,  True, False,  True])"
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = np.array([6, 0, 0, 3, 2, 5, 6])\n",
    "np.in1d(values, [2, 3, 6])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.262239Z",
     "end_time": "2024-04-17T13:23:25.547081Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.4 用于数组的文件输入输出"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "outputs": [],
   "source": [
    "arr = np.arange(10)\n",
    "np.save('some_array', arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.267818Z",
     "end_time": "2024-04-17T13:23:25.549081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load('some_array.npy')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.275645Z",
     "end_time": "2024-04-17T13:23:25.549081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "outputs": [],
   "source": [
    "np.savez('array_archive.npz', a=arr, b=arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.282455Z",
     "end_time": "2024-04-17T13:23:25.549081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "outputs": [
    {
     "data": {
      "text/plain": "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch = np.load('array_archive.npz')\n",
    "arch['b']"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.289832Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "outputs": [],
   "source": [
    "np.savez_compressed('arrays_compressed.npz', a=arr, b=arr)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.294910Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.5 线性代数"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[1., 2., 3.],\n       [4., 5., 6.]])"
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "x"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.302377Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 6., 23.],\n       [-1.,  7.],\n       [ 8.,  9.]])"
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.array([[6., 23.], [-1, 7], [8, 9]])\n",
    "y"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.307232Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 28.,  64.],\n       [ 67., 181.]])"
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(y)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.312653Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 28.,  64.],\n       [ 67., 181.]])"
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, y)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.322518Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 6., 15.])"
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x, np.ones(3))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.328769Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 2.9035,  0.0888, -1.2125,  0.5371,  0.6586],\n       [ 0.0888,  0.1757, -0.3456, -0.1247,  0.0707],\n       [-1.2125, -0.3456,  1.5811,  0.1344, -0.6047],\n       [ 0.5371, -0.1247,  0.1344,  0.4213,  0.1289],\n       [ 0.6586,  0.0707, -0.6047,  0.1289,  0.7222]])"
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.linalg import inv, qr\n",
    "\n",
    "X = np.random.randn(5, 5)\n",
    "mat = X.T.dot(X)\n",
    "inv(mat)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.334266Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ 1.,  0., -0., -0.,  0.],\n       [-0.,  1.,  0.,  0., -0.],\n       [-0., -0.,  1., -0., -0.],\n       [-0.,  0., -0.,  1., -0.],\n       [ 0.,  0., -0., -0.,  1.]])"
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.dot(inv(mat))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.339454Z",
     "end_time": "2024-04-17T13:23:25.550082Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[ -2.3337,  -2.8585,  -4.0336,   5.763 ,  -2.1426],\n       [  0.    , -13.4513,  -2.9266,  -3.6108,  -0.5329],\n       [  0.    ,   0.    ,  -1.1909,   0.7811,  -2.1892],\n       [  0.    ,   0.    ,   0.    ,  -1.6006,   0.49  ],\n       [  0.    ,   0.    ,   0.    ,   0.    ,   0.863 ]])"
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q, r = qr(mat)\n",
    "r"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.345109Z",
     "end_time": "2024-04-17T13:23:25.551082Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.6 伪随机数生成"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[-0.132 , -0.5292,  0.3035, -0.8896],\n       [-0.1733,  0.6433, -1.254 ,  0.1172],\n       [ 0.8665,  1.0795, -0.3975,  1.4875],\n       [ 0.558 ,  0.6144,  0.428 , -0.272 ]])"
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = np.random.normal(size=(4, 4))\n",
    "samples"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.352282Z",
     "end_time": "2024-04-17T13:23:25.587090Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "684 ms ± 5.03 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "from random import normalvariate\n",
    "\n",
    "N = 1_000_000\n",
    "%timeit samples=[normalvariate(0, 1) for _ in range(N)]"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:25.362043Z",
     "end_time": "2024-04-17T13:23:30.908711Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.5 ms ± 683 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit np.random.normal(size=N)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:30.909700Z",
     "end_time": "2024-04-17T13:23:32.990951Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ 0.4714, -1.191 ,  1.4327, -0.3127, -0.7206,  0.8872,  0.8596,\n       -0.6365,  0.0157, -2.2427])"
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1234)\n",
    "rng = np.random.RandomState(1234)\n",
    "rng.randn(10)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:32.989951Z",
     "end_time": "2024-04-17T13:23:32.996599Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 4.7 示例：随机漫步"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1af0fbc0e10>]"
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "position = 0\n",
    "walk = [position]\n",
    "steps = 1000\n",
    "for i in range(steps):\n",
    "    step = 1 if random.randint(0, 1) else -1\n",
    "    position += step\n",
    "    walk.append(position)\n",
    "plt.plot(walk[:100])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:32.998598Z",
     "end_time": "2024-04-17T13:23:33.138418Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x1af0ff33590>]"
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=nsteps)\n",
    "steps = np.where(draws > 0.1, 1, -1)\n",
    "walk = steps.cumsum()\n",
    "plt.plot(walk[:100])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.115414Z",
     "end_time": "2024-04-17T13:23:33.270235Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "outputs": [
    {
     "data": {
      "text/plain": "-9"
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.min()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.235706Z",
     "end_time": "2024-04-17T13:23:33.270235Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "outputs": [
    {
     "data": {
      "text/plain": "60"
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walk.max()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.239301Z",
     "end_time": "2024-04-17T13:23:33.270235Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "outputs": [
    {
     "data": {
      "text/plain": "297"
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.abs(walk) >= 10).argmax()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.247250Z",
     "end_time": "2024-04-17T13:23:33.270235Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### 一次模拟多个随机漫步"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "outputs": [
    {
     "data": {
      "text/plain": "array([[  1,   2,   3, ...,  46,  47,  46],\n       [  1,   0,   1, ...,  40,  41,  42],\n       [  1,   2,   3, ..., -26, -27, -28],\n       ...,\n       [  1,   0,   1, ...,  64,  65,  66],\n       [  1,   2,   1, ...,   2,   1,   0],\n       [ -1,  -2,  -3, ...,  32,  33,  34]])"
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nwalks = 5000\n",
    "nsteps = 1000\n",
    "draws = np.random.randint(0, 2, size=(nwalks, nsteps))\n",
    "steps = np.where(draws > 0, 1, -1)\n",
    "walks = steps.cumsum(1)\n",
    "walks"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.251231Z",
     "end_time": "2024-04-17T13:23:33.399546Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "outputs": [
    {
     "data": {
      "text/plain": "122"
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.max()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.303861Z",
     "end_time": "2024-04-17T13:23:33.412557Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "outputs": [
    {
     "data": {
      "text/plain": "-128"
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "walks.min()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.313109Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "outputs": [
    {
     "data": {
      "text/plain": "array([ True,  True,  True, ...,  True, False,  True])"
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30 = (np.abs(walks) >= 30).any(1)\n",
    "hits30"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.318785Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "outputs": [
    {
     "data": {
      "text/plain": "3368"
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hits30.sum()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.337717Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "outputs": [
    {
     "data": {
      "text/plain": "133"
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crossing_times = (np.abs(walks[hits30]) >= 30).argmax()\n",
    "crossing_times"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.343823Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "outputs": [
    {
     "data": {
      "text/plain": "133.0"
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crossing_times.mean()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.365694Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "start_time": "2024-04-17T13:23:33.370459Z",
     "end_time": "2024-04-17T13:23:33.413559Z"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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